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Question

Find the sum of all natural numbers between $$250$$ and $$1000$$ which are exactly divisible by $$3$$.


Solution

Clearly the numbers between $$250$$ and $$1000$$ which are divisible by $$3$$ are $$252$$, $$255$$, $$258$$,________ $$999$$.
$$\therefore T_n=999=a+(n-1)d=252+(n-1)3$$
$$333=84+n-1$$
$$\therefore n=333-83=250$$
$$\therefore S=\dfrac{n}{2}[a+l]=(250/2)[252+999]$$
$$=125\times 1251=156375$$.

Mathematics

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